In sonic and supersonic flows, Mach waves are formed. The local Mach wave angle is called a Mach angle μ, and it is related to the local Mach number via

(F.1)

Each Mach wave causes an infinitesimal turn of the flow and a corresponding infinitesimal change in fluid pressure, temperature, density, and Mach number. Through infinitely many such waves, that is, Mach waves, flow can turn a finite angle and attain a finite change in static pressure, static temperature, static density, and Mach number. The Prandtl–Meyer function defines an angle (in radians) that a sonic flow has to turn in order to achieve a supersonic Mach number M.

(F.2)

A graphical representation of the Prandtl–Meyer function and the Mach angle is shown.

M	v (deg)	(deg)	M	v (deg)	(deg)	M	v (deg)	(deg)
1.0	0.00	90.00	5.4	80.43	10.67	28	120.2	2.05
1.1	1.34	65.38	5.5	81.25	10.48	29	120.6	1.98
1.2	3.56	56.44	5.6	82.03	10.29	30	120.9	1.91
1.3	6.17	50.28	5.7	82.80	10.10	31	121.2	1.85
1.4	8.99	45.58	5.8	83.54	9.93	32	121.5	1.79
1.5	11.91	41.81	5.9	84.26	9.76	33	121.8	1.74
1.6	14.86	38.68	6	84.96	9.59	34	122.0	1.69
1.7	17.81	36.03	6.2	86.30	9.28	35	122.3	1.64
1.8	20.73	33.75	6.4	87.56	8.99	36	122.5	1.59
1.9	23.59	31.76	6.6	88.76	8.71	37	122.7	1.55
2.0	26.38	30.00	6.8	89.90	8.46	38	122.9	1.51
2.1	29.10	28.44	7	90.97	8.21	39	123.1	1.47
2.2	31.73	27.04	7.5	93.44	7.66	40	123.3	1.43
2.3	34.28	25.77	8	95.63	7.18	50	124.7	1.15
2.4	36.75	24.62	8.5	97.57	6.76	60	125.7	0.95
2.5	39.12	23.58	9	99.32	6.38	70	126.4	0.82
2.6	41.42	22.62	9.5	100.89	6.04	80	126.9	0.72
2.7	43.62	21.74	10	102.32	5.74	90	127.3	0.64
2.8	45.75	20.92	10.5	103.61	5.47	100	127.6	0.57
2.9	47.79	20.17	11	104.80	5.22
3.0	49.76	19.47	11.5	105.88	4.99
3.1	51.65	18.82	12	106.88	4.78
3.2	53.47	18.21	12.5	107.80	4.59
3.3	55.22	17.64	13	108.65	4.41
3.4	56.91	17.10	13.5	109.44	4.25
3.5	58.53	16.60	14	110.18	4.10
3.6	60.09	16.13	14.5	110.87	3.95
3.7	61.60	15.68	15	111.51	3.82
3.8	63.05	15.26	15.5	112.11	3.70
3.9	64.44	14.86	16	112.68	3.58
4.0	65.79	14.48	16.5	113.21	3.47
4.1	67.08	14.12	17	113.71	3.37
4.2	68.33	13.77	17.5	114.18	3.28
4.3	69.54	13.45	18	114.63	3.18
4.4	70.71	13.14	18.5	115.05	3.10
4.5	71.83	12.84	19	115.45	3.02
4.6	72.92	12.56	20	116.2	2.87
4.7	73.97	12.28	21	116.9	2.73
4.8	74.99	12.02	22	117.5	2.61
4.9	75.97	11.78	23	118.0	2.49
5	76.92	11.54	24	118.6	2.39
5.1	77.84	11.31	25	119.0	2.29
5.2	78.73	11.09	26	119.5	2.20
5.3	79.60	10.88	27	119.9	2.12